A274142 -id:A274142 - cp's OEIS frontend

A274148 Number of integers in n-th generation of tree T(-1/3) defined in Comments.

1, 1, 1, 1, 2, 2, 3, 5, 6, 8, 12, 17, 23, 32, 44, 61, 86, 119, 164, 228, 318, 442, 614, 850, 1181, 1643, 2282, 3167, 4398, 6110, 8489, 11790, 16372, 22737, 31584, 43870, 60930, 84622, 117533, 163248, 226742, 314918, 437389, 607498, 843772, 1171927, 1627699

Offset: 0

Clark Kimberling, Jun 11 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			For r = -1/3, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

Kenny Lau, Table of n, a(n) for n = 0..7004

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> -1/3, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

More terms from Kenny Lau, Jul 01 2016

A274149 Number of integers in n-th generation of tree T(-1/4) defined in Comments.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 17, 22, 29, 38, 51, 68, 90, 119, 158, 209, 277, 368, 489, 648, 858, 1137, 1509, 2002, 2655, 3520, 4667, 6189, 8208, 10885, 14436, 19141, 25382, 33659, 44638, 59195, 78497, 104092, 138036, 183050, 242745, 321904, 426875

Offset: 0

Clark Kimberling, Jun 11 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			For r = -1/4, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

Kenny Lau, Table of n, a(n) for n = 0..8153

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> -1/4, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

a(n-1) = length of row n of the array in A274185.

More terms from Kenny Lau, Jul 01 2016

A274150 Number of integers in n-th generation of tree T(-2/3) defined in Comments.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 2, 4, 5, 7, 10, 14, 17, 23, 33, 43, 61, 82, 111, 150, 202, 278, 376, 516, 694, 941, 1281, 1731, 2369, 3208, 4364, 5915, 8015, 10911, 14792, 20139, 27314, 37082, 50358, 68309, 92891, 126054, 171277, 232504, 315584, 428704, 581880, 790589, 1073298, 1457466, 1979119, 2686767, 3649316

Offset: 0

Clark Kimberling, Jun 11 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			For r = -2/3, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

Kenny Lau, Table of n, a(n) for n = 0..7521

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> -2/3, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

More terms from Kenny Lau, Jul 01 2016

A274151 Number of integers in n-th generation of tree T(-3/4) defined in Comments.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 6, 8, 11, 14, 17, 20, 26, 36, 45, 56, 74, 96, 120, 150, 191, 245, 318, 405, 517, 665, 850, 1073, 1364, 1749, 2233, 2860, 3660, 4678, 5970, 7610, 9691, 12357, 15808, 20190, 25815, 32990, 42127, 53730, 68537, 87474, 111636, 142653, 182214, 232784, 297231, 379421

Offset: 0

Clark Kimberling, Jun 11 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			For r = -3/4, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

Kenny Lau, Table of n, a(n) for n = 0..9418

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> -3/4, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

More terms from Kenny Lau, Jul 02 2016

A274152 Number of integers in n-th generation of tree T(3/2) defined in Comments.

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 6, 8, 12, 18, 28, 42, 62, 96, 142, 210, 316, 474, 712, 1070, 1606, 2410, 3608, 5412, 8124, 12184, 18268, 27404, 41114, 61662, 92484, 138702, 208020, 311988, 467928, 701866, 1052812, 1579204, 2368764, 3553048, 5329306, 7993478, 11989564, 17983626, 26974744, 40461664, 60692460

Offset: 0

Clark Kimberling, Jun 11 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			For r = 3/2, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 2.

Kenny Lau, Table of n, a(n) for n = 0..73

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> 3/2, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

More terms from Kenny Lau, Jul 02 2016

A274154 Number of integers in n-th generation of tree T(-3/2) defined in Comments.

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 5, 8, 12, 18, 27, 41, 60, 92, 134, 206, 305, 463, 694, 1041, 1561, 2344, 3506, 5279, 7903, 11877, 17823, 26689, 40100, 60041, 90217, 135312, 202940, 304555, 456295, 685209, 1027291, 1541669, 2312510, 3466919, 5203662, 7801283, 11707295, 17559032, 26334864

Offset: 0

Clark Kimberling, Jun 12 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			For r = -3/2, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 2.

Kenny Lau, Table of n, a(n) for n = 0..72

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> -3/2, {k, 1, z}]; Table[
Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

More terms from Kenny Lau, Jun 30 2017

A274155 Number of integers in n-th generation of tree T(-5/2) defined in Comments.

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 6, 8, 12, 19, 28, 42, 63, 95, 145, 212, 321, 479, 723, 1080, 1622, 2436, 3652, 5472, 8212, 12309, 18488, 27718, 41599, 62370, 93578, 140360, 210511, 315787, 473646, 710583, 1065773, 1598933, 2398260, 3597426, 5395845, 8093416, 12140388, 18210490, 27317995

Offset: 0

Clark Kimberling, Jun 12 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			For r = -5/2, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 2.

Kenny Lau, Table of n, a(n) for n = 0..48

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> -5/2, {k, 1, z}]; Table[
Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}](*A274155*)

More terms from Kenny Lau, Jun 30 2017

A274156 Number of integers in n-th generation of tree T(2^(-1/2)) defined in Comments.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 10, 14, 19, 25, 35, 47, 64, 87, 119, 161, 220, 300, 407, 554, 757, 1028, 1399, 1908, 2598, 3534, 4816, 6560, 8929, 12161, 16567, 22556, 30718, 41843, 56981, 77597, 105693, 143944, 196029, 266991, 363634, 495228, 674481, 918629, 1251106, 1703941, 2320726, 3160713, 4304733

Offset: 0

Clark Kimberling, Jun 12 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			If r = 2^(-1/2), then g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

Kenny Lau, Table of n, a(n) for n = 0..7448

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> 2^(-1/2), {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

More terms from Kenny Lau, Jul 01 2016

A274157 Number of integers in n-th generation of tree T(3^(-1/2)) defined in Comments.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 6, 7, 9, 11, 14, 16, 22, 26, 33, 40, 53, 62, 82, 97, 127, 151, 198, 234, 309, 366, 480, 570, 749, 887, 1165, 1382, 1815, 2153, 2827, 3353, 4405, 5224, 6859, 8137, 10687, 12675, 16646, 19746, 25932, 30761, 40395, 47917, 62929, 74647, 98027, 116285, 152711, 181150

Offset: 0

Clark Kimberling, Jun 12 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			If r = 3^(-1/2), then g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

Kenny Lau, Table of n, a(n) for n = 0..10382

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> 3^(-1/2), {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

More terms from Kenny Lau, Jul 04 2016

A274158 Number of integers in n-th generation of tree T(2^(-1/3)) defined in Comments.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 6, 8, 9, 13, 17, 22, 27, 36, 47, 61, 77, 101, 132, 171, 219, 285, 370, 480, 619, 803, 1042, 1351, 1747, 2264, 2936, 3805, 4927, 6385, 8276, 10725, 13894, 18004, 23333, 30238, 39179, 50770, 65794, 85261, 110483, 143171, 185534, 240432, 311566, 403749, 523216, 678031

Offset: 0

Clark Kimberling, Jun 12 2016

Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.

See A274142 for a guide to related sequences.

			If r = 2^(-1/3), then g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 1.

Kenny Lau, Table of n, a(n) for n = 0..8877

Cf. A274142.

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> 2^(-1/3), {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

More terms from Kenny Lau, Jul 04 2016

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A274148 Number of integers in n-th generation of tree T(-1/3) defined in Comments.

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A274149 Number of integers in n-th generation of tree T(-1/4) defined in Comments.

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A274150 Number of integers in n-th generation of tree T(-2/3) defined in Comments.

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A274151 Number of integers in n-th generation of tree T(-3/4) defined in Comments.

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A274152 Number of integers in n-th generation of tree T(3/2) defined in Comments.

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A274154 Number of integers in n-th generation of tree T(-3/2) defined in Comments.

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A274155 Number of integers in n-th generation of tree T(-5/2) defined in Comments.

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A274156 Number of integers in n-th generation of tree T(2^(-1/2)) defined in Comments.